Problem: Simplify the following expression: $ t = \dfrac{-7z - 5}{9z} + \dfrac{9}{8} $
Answer: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{8}{8}$ $ \dfrac{-7z - 5}{9z} \times \dfrac{8}{8} = \dfrac{-56z - 40}{72z} $ Multiply the second expression by $\dfrac{9z}{9z}$ $ \dfrac{9}{8} \times \dfrac{9z}{9z} = \dfrac{81z}{72z} $ Therefore $ t = \dfrac{-56z - 40}{72z} + \dfrac{81z}{72z} $ Now the expressions have the same denominator we can simply add the numerators: $t = \dfrac{-56z - 40 + 81z}{72z} $ $t = \dfrac{25z - 40}{72z}$